Alternating Groups I

Alternating Groups I

What is this problem about?

The "Alternating Groups I interview question" is a circular array challenge focused on pattern matching. You are given an array representing a ring of colored tiles (e.g., Red and Blue). An "alternating group" is defined as a sequence of three consecutive tiles where the middle tile has a different color than the two tiles flanking it. Because the tiles are in a circle, you must also consider groups that wrap around from the end of the array back to the beginning.

Why is this asked in interviews?

Companies like Meta and Amazon ask the "Alternating Groups I coding problem" to test a candidate's ability to handle circular data structures and boundary conditions. It's a fundamental test of "Array interview pattern" logic, specifically how to use the modulo operator (%) or array padding to simulate a continuous loop without physical pointer manipulation.

Algorithmic pattern used

This problem follows the Sliding Window and Circular Indexing patterns.

1. Looping: Iterate through every index $i$ in the array.
2. Neighbor Access: For each $i$, look at $i-1$ (left) and $i+1$ (right).
3. Circular Logic: Use (i - 1 + n) % n and (i + 1) % n to ensure you stay within the array bounds even at the edges.
4. Validation: Check if color[i] != color[left] and color[i] != color[right].

Example explanation

Colors: [0, 1, 0, 0, 1] (where 0 is Red, 1 is Blue)

• Index 0: Neighbors are 4 (color 1) and 1 (color 1). Current is 0. Group [1, 0, 1] is alternating. (Count = 1)
• Index 1: Neighbors are 0 (color 0) and 2 (color 0). Current is 1. Group [0, 1, 0] is alternating. (Count = 2)
• Index 2: Neighbors are 1 (color 1) and 3 (color 0). Current is 0. Not alternating.
• Index 3: Neighbors are 2 (color 0) and 4 (color 1). Current is 0. Not alternating.
• Index 4: Neighbors are 3 (color 0) and 0 (color 0). Current is 1. Group [0, 1, 0] is alternating. (Count = 3) Total: 3 alternating groups.

Common mistakes candidates make

• Ignoring the Circular Nature: Only checking indices from $1$ to $n-2$ and missing the wrap-around cases at $0$ and $n-1$.
• Redundant Checks: Over-complicating the logic by checking all possible triplets manually instead of iterating through "middle" elements.
• Index Out of Bounds: Forgetting the +n in (i-1+n)%n, which can lead to negative index errors in some languages.

Interview preparation tip

Whenever you see the word "circular" or "ring," immediately think of the modulo operator. Practice problems that involve circular buffers to get comfortable with the transition from the end of an array back to the start.